We first consider the path integral for the general motion of the gravitating two–body system, not specifying yet
either to the near or far zones. In the in–in formalism it is given by [1]}
\(\exp \left[i W(\lbrace \vec{j}_{k,1}\rbrace ,\lbrace \vec{j}_{k,2}\rbrace ,J_1,J_2)\right] ~&=&~\int \prod _{k=1}^2 {\cal D} \vec{x}_{k,1} {\cal D} \vec{x}_{k,1}\exp \Biggl \lbrace i \sum _{k=1}^2 \left(S_{pp}(\vec{x}_{k,1}) -S_{pp}(\vec{x}_{k,2}) \right)\nonumber \\ &&+i \sum _{k=1}^2 \int dt \left(\vec{j}_{k,1}.\vec{x}_{k,1} -\vec{j}_{k,2}.\vec{x}_{k,2} \right)\nonumber \\ &&+ i \int d^Dx {\cal L}_{\rm int}\left[\lbrace \vec{x}_{k,1}\rbrace ,\lbrace \vec{x}_{k,2}\rbrace , -i \delta _{J_1}, -i \delta _{J_2}\right]\Biggr \rbrace  Z_0\left[J_1,J_2\right].\nonumber \\\) 
